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9 triangles of equal area, by 8 points, equilateral - 2023 Chile NMO L1 P3

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May 19, 2024
geometryareasEquilateral

Problem Statement

Let △ABC\vartriangle ABC be an equilateral triangle with side 11. Four points are marked P1P_1, P2P_2, P3P_3, P4P_4 on side ACAC and four points Q1Q_1, Q2Q_2, Q3Q_3, Q4Q_4 on side ABAB (see figure) of such a way to generate 99 triangles of equal area. Find the length of segment AP4AP_4. https://cdn.artofproblemsolving.com/attachments/5/f/29243932262cb963b376244f4c981b1afe87c6.png
PS. Easier version of [url=https://artofproblemsolving.com/community/c6h3323141p30741525]2023 Chile NMO L2 P3
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